Question

What's the LCM of 6 and 8?

Answer 1

24

Explanation:

Method. Find least positive integers L and M such that 6L = 8M.

The common value is LCM.

L = 4 and M = 3 and the LCM = 24.

CMs are N X LCM, N = 1, 2, 3, 4, ... N = 1 gives LCM.

Answer 2

`LCM (6,8) = 3 times 2 times 2 times 2=24`

Explanation:

Step one prime factor.
`6=2 times 3`
`8=2 times 2 times 2`

In order for a number, `X`, to be a multiple of `6` in must "contain" `6`, i.e. be of the form `X= n times 2 times 3`, where `n` is a natural number `(1,2,3, ...)` and similarly for a number, `Y`, to be a multiple of `8` it must be in the form `Y=m times 2 times 2 times 2` where `m` is a natural number. A common multiple is both of these `Z= p times 3 times 2 times 2 times 2`. The LCM has `p=1`.

`LCM (6,8) = 3 times 2 times 2 times 2=24`